Question : The median of an equilateral triangle is $15 \sqrt{3} \mathrm{~cm}$. What is the side of this triangle?
Option 1: 24 cm
Option 2: 18 cm
Option 3: 30 cm
Option 4: 36 cm
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Correct Answer: 30 cm
Solution :
Length of median of the equilateral triangle = $\frac{\sqrt{3}}{2}$ × side
Let the side of the equilateral triangle be a cm.
Length of median of the triangle = $\frac{\sqrt{3}}{2}$ × a
⇒ $\frac{\sqrt{3}}{2}$ × a = 15$\sqrt{3}$
$\therefore$ a = 30 cm
Hence, the correct answer is 30 cm.
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